Stationary Discrete Autoregressive‐moving Average Time Series Generated by Mixtures

Abstract. Two simple stationary processes of discrete random variables with arbitrarily chosen first‐order marginal distributions, DARMA ( p, N + 1) and NDARMA ( p, N ), are given. The correlation structure of these processes mimics that of the usual linear ARMA ( p, q ) processes. The relationship of these processes to mover‐stayer models, and to models for discrete time series given separately by Lindqvist and Pegram is discussed. Ad hoc nonparametric estimators for the parameters in the DARMA ( p, N + 1) and NDARMA ( p, N ) are given. A simulation study shows them to be as good as maximum likelihood estimators for the first‐order autoregressive case, and to be much simpler to compute than the maximum likelihood estimators.